The Light Blues ensured progression from the fifth round on Friday night when they beat fellow League One side Dunfermline Athletic 4-0 at Ibrox.
That sent them into the last eight for the first time in four years and now they’ll host League Two Rovers as they look to continue their run in the event.
Golfer Stephen Gallacher helped conduct the draw this afternoon at Tannadice after Dundee United’s 2-1 win over St Mirren.
As things stand, the tie with the Coatbridge side is due to be played on Saturday, March 8, although that date could change if the fixture is selected for live television coverage.
Ally McCoist’s men have been in impressive form so far in the country’s main knockout tournament.
Beating the Pars two days ago means Gers have now scored nine goals on their run and have still to concede.
They are bidding to win the trophy for the first time since Falkirk were beaten 1-0 in the 2009 final thanks to Nacho Novo’s strike.
And with belief growing among Light Blues fans, many of them will feel their team can go all the way.
Confidence will certainly rise after being paired with Albion, the lowest-ranked side still involved who have gone this far for the first time since 1934.
Of course, Gers beat them in their first game of this season, a 4-0 victory in the first round of the Ramsdens Cup last July at Livingston.
With holders Celtic out and a maximum of four Premiership sides left, the competition is wide open and some bookmakers now have the 54-time Scottish champions as favourites.
McCoist will likely play that down but with both semi-finals taking place at Ibrox on April 12 and 13, there are plenty of incentives for Gers to get through their next tie next month.
In the other games, Raith will play St Johnstone in Kirkcaldy and Aberdeen are at home to Championship outfit Dumbarton.
United’s reward for their win today is a trip to either Stranraer or Inverness, who will replay after a 2-2 draw at Stair Park yesterday.
Progressing to this stage means Rangers’ home League One fixture with Airdrie, also scheduled for March 8, will have to move to another date.
Ticket information for the quarter-final match will be relayed to fans on official club media channels as soon as it is available.
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